When someone asks what you do for a living, what's your answer? If you say anything other than "writer" or "author," it's wrong. You're probably also an employee. Maybe a waitress, or a police officer, a teacher or a stay-at-home mom. But your first answer should always be "writer" or "author." You can add the other thing, too, if you want. As an indie author, you should always be promoting. Start by marketing yourself as the writer you are, right away at the first introduction.
Writer, Author, Indian Chief
According to the cold, hard numbers, indie authors are successful -- in some ways, more so than traditionally-published authors. So you have no reason to shy away from telling people that you're an author, and an indie author to boot. People know about Amanda Hocking and John Locke and Fifty Shades of Grey. So be proud of who you are and what you do. If you present yourself like a professional who has pride in themselves, that's exactly how others will see you.
So what do you do for a living? You're an indie author. Be a smart one, and be prepared to offer information when people ask for more. Give them an easy link or easy names to remember. Give them a bookmark or something physical to hold. Let them see a book cover. You never know who you're going to meet, or what they might like to read. So always present yourself as an author, along with all that other stuff you already are.